Results 1 to 6 of 6

Math Help - Pairing problem

  1. #1
    Member
    Joined
    Mar 2010
    Posts
    75

    Pairing problem

    Each of the 75 children in a line was assigned one of the integers from 1 through 75 by counting off in order. Then, standing in the same order, the children counted off in the opposite direction, so that the child who was assigned the number 75 the first time was assigned the number 1 the second time. Which of the following is a pair of numbers assigned to the same child?

    How can I show and prove that it has to be 47 and 29?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    GJA
    GJA is offline
    Member
    Joined
    Jul 2012
    From
    USA
    Posts
    109
    Thanks
    29

    Re: Pairing problem

    Hi, mjoshua.

    It might help to think about what happens when you add the numbers together that a student received.

    Does this help get things on the right track?

    Good luck!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2010
    Posts
    75

    Re: Pairing problem

    It does not, I'm sorry.. Anyone else?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    GJA
    GJA is offline
    Member
    Joined
    Jul 2012
    From
    USA
    Posts
    109
    Thanks
    29

    Re: Pairing problem

    Just for fun, can you write the two numbers assigned to person number one, the two numbers assigned to person number two, then add each pair of numbers...I think that might move things in the right direction
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Mar 2010
    Posts
    75

    Re: Pairing problem

    So the proof is the pairs must add to 76?? That seems rather bland..?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,660
    Thanks
    600

    Re: Pairing problem

    Hello, mjoshua!

    Each of the 75 children in a line was assigned one of the integers from 1 through 75 by counting off in order.
    Then, standing in the same order, the children counted off in the opposite direction,
    so that the child who was assigned the number 75 the first time was assigned the number 1 the second time.
    Which of the following is a pair of numbers assigned to the same child?

    How can I show and prove that it has to be 47 and 29?

    Take a look at GJA's observation . . .

    . . \begin{array}{c|cccccc} \text{1st count} & 1 & 2 & 3 & \cdots & 74 &75 \\ \hline \text{2nd count} & 75 & 74 & 73 & \cdots & 2 & 1 \end{array}


    Each child received a pair of numbers whose sum is 76.

    Yes, that's kind of bland.
    But when an answer is that simple, don't expect fireworks . . .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Axiom of pairing
    Posted in the Discrete Math Forum
    Replies: 12
    Last Post: June 16th 2011, 03:07 PM
  2. What is a word (side pairing elements)
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: May 28th 2010, 06:32 AM
  3. inverting the Pairing function
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: November 22nd 2009, 11:04 AM
  4. Pairing Senators
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 11th 2009, 10:23 PM
  5. Stats - pairing or unknown o?
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: February 7th 2009, 09:56 PM

Search Tags


/mathhelpforum @mathhelpforum